If the roots of the equation `x^(2) + px+ q = 0` are`x^(2) + px+ q = 0 " are " tan 19^(@) and tan 26^(@),` then which one of the following is correct ?

Options

A. `q-p=1`
B. `p-q=1`
C. `p+q = 2`
D. `p+q = 3`

Answer

A

Explanation

` " Given" , tan19^(@) and tan 26^(@) " are roots of " x^(2) + px + q = 0 `
` :. tan 19^(@) + tan 26^(@) = (-p)/1 = -p`
` (tan 19^(@)) ( tan 26^(@)) = q/1 = q `
` tan( 19^(@)+ 26^(@)) = (tan19^(@)+ tan26^(@))/(1- tan 19^(@) tan 26^(@))`
` tan 45^(@) = -p/(1-q) rArr1 = -p/(1-q)`
`rArr 1-q=-p`
`rArr q-p=1`